Notes: 6.1 and 6.2
Geometry: Ratios and Proportions
Name:______________________
Date:__________ Period:______
Definition of a ratio:_______________________________________________________
______________________________________________________________________.
You must simplify ratios!!!! (Reduce all fractions!)
Conversions you must know:
Metric
US Customary - Weight
US Customary - Capacity
US Customary - Length
Examples
1.
Simplify the ratios.
1m
a.
__________
2 km
b.
3 yds
__________
6 ft
c.
2 gallons
5 quarts
e.
9 inches
2 yards
d.
10 feet
2 inches
2.
The perimeter of an isosceles triangle shown is 56 inches.
The ratio of LM : MN is 5:4. Find the lengths of the sides
and the base of the triangle.
3.
The measures of a triangle are in the extended ratio
3:4:8. Find the measures of the angles.
__________
________
________
L
N
M
1
Definition of a proportion:__________________________________________________
______________________________________________________________________.
Properties:
a) cross-products:
b)
where ______________
____________________
____________________
____________________
____________________
reciprocals:
c)
d)
4) Solve the proportion.
9 6
a)
________

14 x
c)
8 14

b 5
__________
b)
s 5 s
__________

4
10
d)
3 x x

_________
6
2
5) A photo of a building has the measurements given in the sketch below. The actual
1
7
building is 26 feet wide. How tall is it? ________
4
8 inches
What is the height of the door? ________
2.75 inches
1
inch
2
6) The ratio of the side lengths of QRS to the corresponding side lengths of VTU
are 3:2. Find all unknown lengths.
U
T
2 cm
Q
V
S
18 cm
R
2
7) The ratios of side lengths of DEF to the corresponding side lengths of GHI are
1:3. If the base and the height of DEF are 8 and 4 respectively, find the area of
GHI .
8) In a photograph taken from an airplane, a section of a city street is 3.5 inches long
1
and
of an inch wide. If the actual street is 30 feet wide, how long is it?
8
_____________________
What distinguishes a ratio from other quotients?________________________________
______________________________________________________________________.
How do you solve
proportions?________________________________________________.
In one town, the ratio of cats to dogs is 3:2 and the ratio of cats to rabbits is 18:1.
What is the ratio of dogs to rabbits? (Sounds like an SAT question to me ).
____________
9) Tell whether the statement is true.
s 15
s 3

a) If
then  .
10 t
t 2
c) If
10) Find the length of LQ.
11) Find the length of PN.
b) If
3 5
3 x 5 y
then


x y
x
y
3 d
3b d  7


then
b 7
d
b
M
6
N
15
13
L
5
Q
P
12) You are building a scale model of your uncle’s fishing boat. The boat is 62 feet
long and 23 feet wide. The model will be 14 inches long. How wide should it be? If
the mast is 30 feet tall, how tall should the mast be in the model?
3
Geometric Mean
The geometric mean of two positive numbers__________________________________
______________________________________________________________________.
13) Find the geometric mean between:
a) 4 and 9 _________
b) 3 and 4 _____________ c) 6 and 8 _____________
Homework:
6.1: Page 360-361 3-10, 11-45 odd,52,53, 57, 59, 65
6.2: Page 367 3-14, 16-18, 22-24, 28-29
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